含二项式系数、二重因子和升因子的多项式恒等式及其概率解释和证明
Polynomial identities that involve binomial coefficients, double and rising factorials and their probabilistic interpretations and proofs
摘要：
我们制定了几个多项式的身份。这些恒等式的一面有一个很好的简单形式。而另一种具有多项式的形式，其系数包含二项式系数双因子或（和）上升因子。这些身份的起源和证明是概率。然而，它们的形式表明在简化表达式方面的普遍应用。文中还提出了许多有用的简化公式。
英文摘要：
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The origins and the proofs of these identities are probabilistic. However, their form suggests universal applications in simplifying expressions. Many useful simplifying formulae are presented in the sequel.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
